Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

find the unit vector in the same direction as $v$ $v = 3 i - 4 j$

The unit vector in the direction of the vector $v = 3 i - 4 j$ is $u = \frac{3}{5} i - \frac{4}{5} j$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given data

The given vector is

$v = 3 i - 4 j$

Step 2. Finding the magnitude of the given vector

The magnitude of the vector $v = 3 i - 4 j$ is

$|v| = \sqrt{{(3)}^{2} + {(- 4)}^{2}} \Rightarrow |v| = \sqrt{9 + 16} \Rightarrow |v| = \sqrt{25} \Rightarrow |v| = 5$

Step 3. Finding the unit vector

The unit vector $u$ in the direction of $v$ is:

$u = \frac{v}{||v||}$

Substitute the values of vector and magnitude vector in the formula.

$u = \frac{3 i - 4 j}{|5|} \Rightarrow u = \frac{3}{5} i - \frac{4}{5} j$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

find the unit vector in the same direction as $v$ $v = 3 i - 4 j$

Step by Step Solution

Step 1. Given data

Step 2. Finding the magnitude of the given vector

Step 3. Finding the unit vector

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

find the unit vector in the same direction as v v=3i-4j

Step by Step Solution

Step 1. Given data

Step 2. Finding the magnitude of the given vector

Step 3. Finding the unit vector

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find the unit vector in the same direction as $v$ $v = 3 i - 4 j$